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Question Number 167750 by mathlove last updated on 24/Mar/22

Answered by Rasheed.Sindhi last updated on 24/Mar/22

$$f(x-y)=f\left(x\right)-f\left(y\right);f\left(2\right)=5;f\left(16\right)=?$$$$\bullet x=2y$$$$f(2y-y)=f\left(2y\right)-f\left(y\right)$$$$f\left(y\right)=f\left(2y\right)-f\left(y\right)$$$$2f\left(y\right)=f\left(2y\right)$$$$\bullet 2y=x\Rightarrow y=\frac{x}{2}$$$$f\left(x\right)=2f\left(\frac{x}{2}\right)$$$$f\left(16\right)=2f\left(8\right)=2\times 2f\left(4\right)=2\times 2\times 2f\left(2\right)$$$$=8\times 5=40$$

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